Unidirectional fibers

The ply density is computed as:

\rho = V^f \rho^f + V^m \rho^m

Young’s modulus in the fiber direction is computed as:

E_1 = V^f E_1^f + V^m E^m

Young’s modulus perpendicular to the fiber direction is calculated with the mechanics of materials approach:

\frac{1}{E_2} = \frac{V^f}{E_2^f} + \frac{V^m}{E^m}

Young’s modulus in the direction perpendicular to the ply (normal to the laminate) is assumed to be equal to the Young’s modulus perpendicular to the fibers:

E_3 = E_2

The major Poisson’s ratio is defined as:

\nu_{12} = V^f \nu_{12}^f + V^m \nu^m

The Poisson’s ratio in the 13 direction is assumed to be equal to the major Poisson’s ratio:

\nu_{13} = \nu_{12}

The Poisson’s ratio in the 23 direction is assumed to be equal to the Poisson’s ratio of the matrix:

\nu_{23} = \nu_m

The shear modulus G12 is calculated as follows:

\frac{1}{G_{12}} = \frac{V^f}{G_{12}^f} + \frac{V^m}{G^m}

The shear modulus G13 is assumed to be equal to G12:

G_{13}=G_{12}

The shear modulus G23 is assumed to be equal to he shear modulus of the matrix:

G_{23}=G_m

The ply thermal conductivity in the fiber direction is computed as:

K_1 = V^f K_1^f + V^m K^m

The thermal conductivity perpendicular to the fiber direction is calculated with the following equations [2]:

\zeta = \frac{1}{4 - 3 V^m}

\eta = \frac{\frac{K_1^f}{K^m} - 1}{\frac{K_1^f}{K^m} + \zeta}

K_2 = K^m \frac{1+\zeta \eta V^f}{1 - \eta V^f}

The thermal conductivity in the direction perpendicular to the ply is assumed to be identical to the thermal conductivity perpendicular to the fibers:

K_3=K_2

The coefficients of thermal expansion, the following equations [3] are used:

\alpha_1 = \frac{(\alpha_1^f E_1^f - \alpha^m E^m)V^f + \alpha^m E^m}{(E_1^f - E^m)V^f + E^m}

\alpha_2 = \alpha^m + (\alpha_2^f - \alpha^m)V^f + (\frac{E_1^f \nu^m - E^m \nu_{12}^f}{E_1})(\alpha^m - \alpha_1^f)V^m V^f

The coefficient of thermal expansion perpendicular to the fibers is assumed to be the same as the matrix thermal expansion coefficient:

\alpha_3 = \alpha_2

The heat capacity is given by:

c_p = \frac{1}{\rho}(V^f \rho^f c_p^f + V^m \rho^m c_p^m)

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